Invariants
Base field: | $\F_{83}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 28 x + 349 x^{2} - 2324 x^{3} + 6889 x^{4}$ |
Frobenius angles: | $\pm0.0829582297929$, $\pm0.306761272556$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.834353.1 |
Galois group: | $D_{4}$ |
Jacobians: | $34$ |
Isomorphism classes: | 34 |
This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4887$ | $46871217$ | $327164085504$ | $2252457124903449$ | $15515857998623455047$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $56$ | $6804$ | $572180$ | $47461796$ | $3938994136$ | $326939362182$ | $27136044280744$ | $2252292265177924$ | $186940256504422316$ | $15516041201682604884$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 34 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=53x^6+79x^5+76x^4+62x^3+10x^2+26x+1$
- $y^2=8x^6+19x^5+41x^4+60x^3+71x^2+48x+80$
- $y^2=28x^6+45x^5+44x^4+39x^3+42x^2+40x+27$
- $y^2=43x^6+35x^5+59x^4+44x^3+15x^2+7x+6$
- $y^2=49x^6+37x^5+78x^4+21x^3+x^2+78x+55$
- $y^2=15x^6+73x^5+16x^4+49x^3+80x^2+65x+48$
- $y^2=43x^6+24x^5+31x^4+58x^3+35x^2+58x+24$
- $y^2=8x^6+43x^5+74x^4+53x^3+38x^2+14x+29$
- $y^2=56x^6+66x^5+16x^4+52x^2+19x+52$
- $y^2=32x^6+60x^4+14x^3+16x^2+28x+22$
- $y^2=80x^6+68x^4+12x^3+20x^2+66x+14$
- $y^2=31x^6+4x^5+31x^4+42x^3+65x^2+82x+19$
- $y^2=15x^6+76x^5+44x^4+47x^3+51x^2+42x+14$
- $y^2=5x^6+54x^5+70x^4+x^3+22x^2+34x+77$
- $y^2=47x^6+51x^5+37x^4+62x^3+22x^2+15x+39$
- $y^2=13x^6+10x^5+34x^4+74x^3+38x^2+67x+54$
- $y^2=77x^6+67x^5+40x^4+63x^3+82x^2+43x+32$
- $y^2=44x^6+76x^5+6x^4+58x^3+53x^2+28x+47$
- $y^2=24x^6+47x^5+10x^4+36x^3+72x^2+15x+54$
- $y^2=14x^6+11x^5+4x^4+11x^3+8x^2+73x+44$
- and 14 more
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{83}$.
Endomorphism algebra over $\F_{83}$The endomorphism algebra of this simple isogeny class is 4.0.834353.1. |
Base change
This is a primitive isogeny class.
Twists
Below is a list of all twists of this isogeny class.
Twist | Extension degree | Common base change |
---|---|---|
2.83.bc_nl | $2$ | (not in LMFDB) |